If you do have this experience, then the songwriter has accomplished their job.
A good working definition of a song is they are a participatory form of music, wherein we songwriters write the music and structure it in a particular way so that the topline (the main melody or idea), hooks you in and makes you the main character of the music, so you can experience the story/experience/feelings we songwriters are trying to share with you.
Ever had a bad break up and notice that all breakup and love songs are suddenly about you? That's not a coincidence.
The audience is as much a part of the song as the artist and songwriters are.
So if you feel a song is about you, the songwriter did their job well. They made you feel something.